Question

The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 15 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 13 minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is 11 minutes. Use α=0.05

Required:
a. State the hypotheses.
b. What is the p-value?
c. Using α=0.05, can you conclude that the actual mean waiting time is significantly less than the claim of 15 minutes made by the taxpayer advocate.

Answer 1

a)Null hypothesis :
`H_0:\mu \geq 15`

Alternate hypothesis :
`H_a:\mu < 15`

b)p value = 0.1003

c)We can conclude that the actual mean waiting time is significantly less than the claim of 15 minutes made by the taxpayer advocate.

Explanation:

Null hypothesis :
`H_0:\mu \geq 15`

Alternate hypothesis :
`H_a:\mu < 15`

`\mu = 15\\\bar{x}=13\\\sigma = 11\\n = 50`

Sample size is more than 30 . So, we will use Z test

`Z=(x-\mu)/((\sigma)/(√(n)))\\Z=(13-15)/((11)/(√(50)))\\Z=-1.285`

Use z table to find p value

p value = 0.1003

α=0.05

p value< α

So, we reject null hypothesis

Hence We can conclude that the actual mean waiting time is significantly less than the claim of 15 minutes made by the taxpayer advocate.